I need help please on finding equilibrium

Question

The demand function of a certain brand of phones is p+2q=100, and the supply for these phones is 35p-20q=350

Find the equilibrium.

Answer 1

Equilibrium occurs when supply equals demand, which occurs where the two lines cross.  Find the crossing point by solving the system of two equations.  I'll use the elimination (addition) method:

 

   p +  2q = 100

35p - 20q = 350

 

Let's eliminate the q variable by multiplying the first equation by 10 the adding the two equations:

 

   (p + 2q = 100)*(10)
35p - 20q = 350

 

   10p + 20q = 1000

+ 35p  - 20q =  350

---------------------

45p +   0  = 1350

45p = 1350

p = 30

 

To find q:

 

p + 2q = 100

30 + 2q = 100

2q = 70

q = 35

 

Equilibrium occurs when p = 30, q = 35